# Stable and unstable equilibrium

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A metal ball (mass m) with a hole through it is threaded on a frictionless horizontal rod. A massless stirring (length l) attached to the ball runs over and massless, frictionless pully and supports a block of mass M. (a) Write down the potential energy U(ᶿ). (The PE is given easily in terms of the heights shown as H and h. Estimate these two variables in favor of ᶿ and the constant b and l. Assume that the pulley and ball have negligible size). b) by differentiating U(ᶿ) find whether this system has an equilibrium position, and for what values of M and m equilibrium can occur. Discuss the stability of any equilibrium positions.

I have done problems similar to this but not with quite this set up. Outline of solution please.

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Two masses connected by string and pulley and to consider the condition for equilibrium.

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